Related papers: Integrability of quantum dots
In this paper we consider quantum Hamiltonians with time-dependent interaction strengths, and following the recently formulated generalized Bethe ansatz framework [P. R. Pasnoori, Phys. Rev. B 112, L060409 (2025)], we show that constraints…
In this work, we show that the completeness relation for the eigenvectors, which is an essential assumption of quantum mechanics, remains true if the Hamiltonian, having a discrete spectrum, is modified by a delta potential (to be made…
Using deformation quantization and suitable 2 by 2 quantum $R$-matrices we show that a list of Toda like classical integrable systems given by Y.B.Suris is quantum integrable in the sense that the classical conserved quantities (which are…
A new integrable generalization to the 2D sphere $S^2$ and to the hyperbolic space $H^2$ of the 2D Euclidean anisotropic oscillator Hamiltonian with Rosochatius (centrifugal) terms is presented, and its curved integral of the motion is…
We investigate the asymptotic stability and ergodic properties of quantum trajectories under imperfect measurement, extending previous results established for the ideal case of perfect measurement. We establish a necessary and sufficient…
We consider wavefunctions which are non-negative in some tensor product basis. We study what possible teleportation can occur in such wavefunctions, giving a complete answer in some cases (when one system is a qubit) and partial answers…
In this paper, we investigate the asymptotic stability of finite-dimensional stochastic integrable Hamiltonian systems via information entropy. Specifically, we establish the asymptotic vanishing of Shannon entropy difference (with…
In this paper we quantize the $N$-dimensional classical Hamiltonian system $H= \frac{|q|}{2(\eta + |q|)} p^2-\frac{k}{\eta +|q|}$, that can be regarded as a deformation of the Coulomb problem with coupling constant $k$, that it is smoothly…
We consider a Hamiltonian system which has its origin in a generalization of exact renormalization group flow of matrix scalar field theory and describes a non-linear generalization of the shock-wave equation that is known to be integrable.…
We discuss the 4-dimensional Hamiltonian systems that describe waves over underwater banks and ridges. The systems are exactly integrable in terms of elliptic functions and of solutions to nontrivial transcendental equations involving the…
In recent paper Fakkousy et al. show that the 3D H\'{e}non-Heiles system with Hamiltonian $ H = \frac{1}{2} (p_1 ^2 + p_2 ^2 + p_3 ^2) +\frac{1}{2} (A q_1 ^2 + C q_2 ^2 + B q_3 ^2) + (\alpha q_1 ^2 + \gamma q_2 ^2)q_3 + \frac{\beta}{3}q_3…
An integrable generalization on the two-dimensional sphere S^2 and the hyperbolic plane H^2 of the Euclidean anisotropic oscillator Hamiltonian with "centrifugal" terms given by $H=1/2(p_1^2+p_2^2)+ \delta q_1^2+(\delta + \Omega)q_2^2…
We show that, in general, averaging at simple resonances a real--analytic, nearly--integrable Hamiltonian, one obtains a one--dimensional system with a cosine--like potential; ``in general'' means for a generic class of holomorphic…
We present non-perturbative solutions for multi-level quantum dot structures coupled to interacting one-dimensional electrodes out of equilibrium. At a special correlation strength the Hamiltonian can be mapped to the Kondo problem which…
This paper investigates the geometry of a completely integrable gradient system defined on the three parameter bivariate beta statistical manifold of the first kind. We prove that the associated vector field is Hamiltonian and admits a Lax…
In this note, we consider the dynamics associated to an epsilon-perturbation of an integrable Hamiltonian system in action-angle coordinates in any number of degrees of freedom and we prove the following result of "micro-diffusion": under…
The superintegrability of several Hamiltonian systems defined on three-dimensional configuration spaces of constant curvature is studied. We first analyze the properties of the Killing vector fields, Noether symmetries and Noether momenta.…
We study the spectral properties of a spin-boson Hamiltonian that depends on two continuous parameters $0\leq\Lambda<\infty$ (interaction strength) and $0\leq\alpha\leq\pi/2$ (integrability switch). In the classical limit this system has…
We show that any soliton solution of an arbitrary two-dimensional integrable equation has the potential to eventually evaporate and emit the exact analogue of Hawking radiation from black holes. From the AKNS matrix formulation of…
In this study, we investigate two distinct classes of normal geodesic flows associated with the left-invariant sub-Riemannian metric on the (2n + 1)-dimensional Heisenberg group. The first class arises from the left-invariant distribution,…